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Hydrol. Earth Syst. Sci., 18, 4485–4507, 2014
www.hydrol-earth-syst-sci.net/18/4485/2014/
doi:10.5194/hess-18-4485-2014
© Author(s) 2014. CC Attribution 3.0 License.
Assimilation of satellite data to optimize large-scale hydrological
model parameters: a case study for the SWOT mission
V. Pedinotti1,2 , A. Boone1 , S. Ricci3 , S. Biancamaria4 , and N. Mognard2
1 CNRM/GAME,
Météo-France, CNRS, URA 1357, Toulouse, France
National d’études spatiales (CNES), Toulouse, France
3 CERFACS/URA 1875, 42 Avenue Gaspard Coriolis, 31057 Toulouse CEDEX, France
4 CNRS, LEGOS, UMR5566 CNRS-CNES-IRD-Université Toulouse III, France
2 Centre
Correspondence to: V. Pedinotti ([email protected])
Received: 3 March 2014 – Published in Hydrol. Earth Syst. Sci. Discuss.: 30 April 2014
Revised: 20 September 2014 – Accepted: 23 September 2014 – Published: 10 November 2014
Abstract. During the last few decades, satellite measurements have been widely used to study the continental water
cycle, especially in regions where in situ measurements are
not readily available. The future Surface Water and Ocean
Topography (SWOT) satellite mission will deliver maps of
water surface elevation (WSE) with an unprecedented resolution and provide observation of rivers wider than 100 m and
water surface areas greater than approximately 250 × 250 m
over continental surfaces between 78◦ S and 78◦ N. This
study aims to investigate the potential of SWOT data for
parameter optimization for large-scale river routing models. The method consists in applying a data assimilation approach, the extended Kalman filter (EKF) algorithm, to correct the Manning roughness coefficients of the ISBA (Interactions between Soil, Biosphere, and Atmosphere)-TRIP
(Total Runoff Integrating Pathways) continental hydrologic
system. Parameters such as the Manning coefficient, used
within such models to describe water basin characteristics,
are generally derived from geomorphological relationships,
which leads to significant errors at reach and large scales. The
current study focuses on the Niger Basin, a transboundary
river. Since the SWOT observations are not available yet and
also to assess the proposed assimilation method, the study
is carried out under the framework of an observing system
simulation experiment (OSSE). It is assumed that modeling
errors are only due to uncertainties in the Manning coefficient. The true Manning coefficients are then supposed to be
known and are used to generate synthetic SWOT observations over the period 2002–2003. The impact of the assimilation system on the Niger Basin hydrological cycle is then
quantified. The optimization of the Manning coefficient using the EKF (extended Kalman filter) algorithm over an 18month period led to a significant improvement of the river
water levels. The relative bias of the water level is globally
improved (a 30 % reduction). The relative bias of the Manning coefficient is also reduced (40 % reduction) and it converges towards an optimal value. Discharge is also improved
by the assimilation, but to a lesser extent than for the water levels (7 %). Moreover, the method allows for a better
simulation of the occurrence and intensity of flood events in
the inner delta and shows skill in simulating the maxima and
minima of water storage anomalies, especially in the groundwater and the aquifer reservoirs. The application of the assimilation method in the framework of an observing system
simulation experiment allows evaluating the skill of the EKF
algorithm to improve hydrological model parameters and to
demonstrate SWOT’s promising potential for global hydrology issues. However, further studies (e.g., considering multiple error sources and the difference between synthetic and
real observations) are needed to achieve the evaluation of the
method.
1
Introduction
The impact of climate variability on land water storage is
becoming an increasingly crucial issue for the development
of future water resource management strategies. In order
to investigate this impact, continental hydrologic systems
(CHSs) can be used to simulate water dynamics above and
Published by Copernicus Publications on behalf of the European Geosciences Union.
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below the land surface as a response to environmental forcing. CHSs are generally made of a land surface model (LSM)
which computes the water and energy budget at the surface–
atmosphere interface, coupled with a river routing model
(RRM) which distributes the runoff to the river and the soil
storage components. At regional or global scales, the realistic representation of major surface hydrologic and hydrodynamic processes is very challenging and requires the use
of computationally efficient, easily parameterized, comparatively simple and physically based routing methodologies.
However, land surface hydrologic processes are highly heterogeneous in space and time and are therefore difficult to parameterize given the huge dimensions of atmospheric general
circulation model (AGCM) grid areas. Observational data describing the water dynamics and storage variations are required to evaluate CHS-simulated diagnostics, and to calibrate these models. In situ data have been extensively used,
but they are limited by their temporal and spatial coverage.
In addition to the information provided by in situ measurements, satellite remote sensing instruments have been developed and are continually improved. These instruments generally provide a large spatial coverage which is more appropriate for global applications, especially in areas where in
situ data are scarce. Such areas are generally sparsely inhabited, with reduced infrastructures and possible geopolitical
issues, such as large portions of the African continent or part
of the Arctic (Alsdorf et al., 2007). Applications using satellite remote sensing techniques lead to many promising perspectives for improving the observation of land surface and
hydrological variables and processes.
Hydrological models require information about continental water dynamics and storage variations above and below
the surface for calibration and evaluation of the simulated
water budget. To this end, diverse types of monitoring data
are needed. In situ discharge data, for example, give information of 1 spatial dimension, which quantifies water fluxes
in a specific river channel, but do not give any direct information about runoff or lateral inflow. Yet, hydrologically
complex areas, such as wetlands and floodplains which are
processes of three spatial dimensions, cannot be adequately
resolved using observations of 1 spatial dimension (Alsdorf
et al., 2007). Spatially distributed observations are required,
such as those provided by satellites which give 2-dimensional
information about surface water dynamics. Recently, efforts
have been made to build global maps of floodplain variability
and extent, providing an additional metric for CHS evaluation (Papa et al., 2010). Nadir altimetry has also constituted a
valuable progress for the monitoring of surface water dynamics and elevation (TOPEX/Poseidon, Envisat, Jason 1 and 2;
Baup et al., 2007; Santos Da Silva et al., 2012).
Although useful, current satellite altimetry spatial resolution does not resolve small-scale land water dynamics
thereby limiting our understanding of large-scale hydrologic
and hydrodynamic processes. The future NASA–CNES–
CSA Surface Water and Ocean Topography (SWOT) satelHydrol. Earth Syst. Sci., 18, 4485–4507, 2014
V. Pedinotti et al.: Assimilation of SWOT data
lite mission will be launched in 2020 and will deliver maps
of water surface elevation (WSE), slope and extent with an
unprecedented resolution of 100 m.
For continental hydrology, the SWOT mission has the potential to help deal with critical issues, such as monitoring
transboundary basins and the development of management
strategies in a changing world. It is necessary to determine
how the SWOT data can be used to improve hydrological
simulations and to better predict continental water storage.
Data assimilation (DA) has been shown to be a promising technique for improving river modeling (Andreadis et al.,
2007; Durand et al., 2010; Biancamaria et al., 2011; Yoon
et al., 2012). Commonly used in operational meteorology
and oceanography, DA combines data coming from various
sources, such as numerical models or observations, while
taking into account measurement errors and model uncertainties for a better description and prediction of the system.
However, these methods are not yet extensively used in hydrology and related works are rare, especially for large-scale
applications. Drusch et al. (2009) used observations of 2 m
air temperature and soil moisture to evaluate a Kalman filterbased soil moisture analysis system and its impact on the
operational ECMWF (European Centre for Medium-Range
Weather Forecasts)-integrated forecast system. They showed
that the impact of EKF on the forecast skill of the operational
weather forecast model was neutral in terms of forecast score
but gave the promising possibility to better constrain the soil
water content with more accurate soil moisture estimates.
Pereira-Cardenal et al. (2011) investigated the potential of
using Envisat water levels observations in a real time or nearreal time by applying an ensemble Kalman filter in order
to update semidistributed hydrological model state variables.
The method was applied to the Syr Darya River basin, a complex mountainous region covering approximately 7000 km2 .
They showed that data assimilation allowed for a better realtime estimation of reservoir levels over the region. However,
because of the state updating procedure used in this study,
which consisted in adding or abstracting water from reservoirs, the method is limited to medium-range forecasting. It
is not suitable for long-term water resources scenario calculations, where mass balance has to be maintained. More recently, Michailovsky et al. (2013) used radar altimetry data
from the Envisat mission for updating the storage of a routing
model of the main reach of the Brahmaputra River driven by
the outputs of a calibrated rainfall–runoff model showing the
potential for the use of altimetric data in combination with
hydrological models for flow modeling in large rivers.
However, in situ flow data were required for the calibration of the rainfall–runoff model which may still be a limitation in some areas with poor data availability such as the
Niger River. Salamon and Feyen (2009) used the residual resampling particle filter to assess parameter, precipitation and
predictive uncertainty in the distributed rainfall–runoff hydrological model LISFLOOD for the Meuse catchment using discharge measurements. They showed that the equifiwww.hydrol-earth-syst-sci.net/18/4485/2014/
V. Pedinotti et al.: Assimilation of SWOT data
Figure 1. The Niger River basin. The spatial resolution is
0.5◦ × 0.5◦ . The red contour marks the boundary of the Niger
Basin. The squares correspond to the following locations: (1) Banankoro, (2) Koulikoro, (3) Ke Macina, (4) Niamey, (5) Ansongo,
(6) Kandadji, (7) Malanville and (8) Lokoja. Terrain elevations
come from ETOPO2 (m).
nality hypothesis (several different parameter sets can lead to
a good estimation of the discharge) was a limitation to the
correction of a distributed hydrological parameter even in a
physically based hydrologic model. Moreover, they emphasized the strong effect of rainfall uncertainties on the analysis. Finally, the results showed that accounting for parameter uncertainty only during a calibration phase was not sufficient to properly predict uncertainty, limiting the application of the method for hydrologic forecasting over longer
time periods. The aforementioned applications of DA in hydrological modeling have shown the potential of using remote sensing data in order to improve the model states or
the parameters. However, they also showed the limitations
due to the generally low spatial and temporal resolutions of
these data sets. Hydrological model uncertainties can come
from several sources, such as model structure, input parameters or input data (mostly precipitation), leading to the development of different DA methodologies. Depending on the
study, DA either aims at optimizing the model input parameters or at directly correcting the model state (generally done
in operational forecast applications for example). The current study investigates benefits of assimilating SWOT virtual
water levels in order to improve input parameters of a largescale hydrological model within the context of a prelaunch
study. The domain study area is the transboundary Niger
Basin (Fig. 1) which crosses a large part of the Sahel and
is a critical source of water in this semiarid region. The West
African region is also characterized by an increasing population, putting larger pressure on the already limited freshwater resources. The hydrology of this basin is modulated by
the West African monsoon (WAM) seasonal and interannual
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variability which is characterized by extreme events such as
droughts and floods which can have dramatic impacts on society and the regional economy. However, the lack of field
measurements limits the understanding of the salient hydrological processes in the Niger Basin. For these reasons, it is
an ideal test bed for studying global hydrological issues. In
a previous study, a Niger Basin hydrological model application was set up using the ISBA (Interaction Sol-AtmosphereBiosphere)-TRIP (Total Runoff Integrating Pathways) distributed hydrological model. Along with river routing, this
model includes a flooding scheme and a linear unconfined
aquifer reservoir (Pedinotti et al., 2012). The model parameters were estimated using geomorphologic relationships to
characterize the river characteristics. The modeling evaluation showed that the model was able to reasonably reproduce the major hydrologic and hydrodynamic processes. The
model outputs were compared to in situ discharge as well as
satellite-derived flood extent, total continental water storage
changes and river height changes. The importance of floodplains was also demonstrated, since they have a considerable
impact on discharge downstream of the inland Niger Delta.
The confined aquifer improves the recession law, i.e., the
curve of the decreasing flow and the simulation of low flows.
However, some model deficiencies remain which can be due
to forcing or model uncertainties; among these sources of
error are the uncertainties of TRIP hydrological parameters.
Indeed, these distributed parameters are defined by empirical
relationships using available observations which are adapted
towards obtaining the best results over the entire globe. However, such relationships might not give the best results locally
(for a particular basin). Studies showed that empirical equation does not work well even within one basin and significant
errors can be found at subbasin or reach scales (e.g., Miller
et al., 2014; Yamazaki et al., 2014). These relationships thus
lead to nonnegligible errors which could be reduced using
satellite data. Such data can potentially be used to estimate
spatial parameters for each particular basin and then contribute to the development of a global database describing
major river characteristics. Pedinotti et al. (2012) performed
sensitivity tests to determine the main sources of uncertainty
among the TRIP parameters. These tests have shown that the
model was sensitive to modifications of some key river parameters (river height and depth as well as Manning coefficient) and that a good estimation of those parameters was
required to optimize the simulation errors. The aim of the
current study is to investigate how SWOT water level products can be used to optimize the Manning coefficient. Unlike
river depth and width, which can be estimated through direct measurements, the Manning coefficient can be estimated
only indirectly, using bathymetry and flow velocity measurements. Several studies have discussed the importance and
difficulty of estimating the Manning coefficient (Chow et
al., 1989; Bates and de Roo, 2000). The sensitivity of the
Manning equation to several river parameters including the
roughness coefficient was investigated by Pistocchi and PenHydrol. Earth Syst. Sci., 18, 4485–4507, 2014
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V. Pedinotti et al.: Assimilation of SWOT data
Figure 2. The TRIP model configuration in ISBA.
nington (2006). In addition to the concern about accurately
estimating the Manning coefficient value, they highlighted
the importance of considering its spatial distribution instead
of a unique value as it is done in some hydrological models
(Arora and Boer, 1999). Moreover, the Manning coefficient
is often used as an adjustment variable for model calibration
which can lead to additional errors (e.g., Biancamaria et al.,
2009). Hunter et al. (2007) indicated that very frequently in
models errors on topography and roughness dominate errors
from equation approximation. The estimation of the Manning coefficient is thus considered in the literature as one
of the major issues limiting the performance of hydrological models and, to the authors knowledge, there have been
very few attempts to evaluate the potential of satellite data
to correct it. Therefore, it was chosen as the main parameter to be investigated in the DA study presented in this study.
Since SWOT observations are not yet available and to assess
the usefulness of data assimilation, this study is carried out
within the framework of an OSSE (observing system simulation experiment) using the TRIP model for the simulation of
the Niger hydrodynamics. SWOT virtual measurements are
produced using a reference ISBA-TRIP simulation. Here, it
is assumed that modeling errors are only due to one key parameter which cannot be directly estimated via observational
data: the Manning roughness coefficient (the other sources
of modeling errors are not considered here, and the reasons
will be explained in Sect. 4.1). The impact of the assimilation
system on the Niger River model is then quantified. First, a
brief presentation of the study domain and the model is made
in Sect. 2. In this section, the Manning coefficient is also defined and its spatial distribution used for the true simulation
is shown. Then, the production of the SWOT virtual water
level is described in Sect. 3. The methodology used to build
the assimilation scheme is explained, and the main variables
of the assimilation problem are described in Sect. 4. Finally,
the impact of the assimilation on the main hydrological variables of the Niger Basin is discussed in Sect. 5.
Hydrol. Earth Syst. Sci., 18, 4485–4507, 2014
2
2.1
Study domain and model description
The Niger River basin
Originating in the Guinean highlands within the Upper Guinea (Haute Guinée) and Forested Guinea (Guinée
Forestière) regions located in the Fouta Djallon mountain
range, the Niger River is the third longest river in Africa
(4200 km), after the Nile and the Congo. Its outlet is located
in Nigeria, discharging through a massive delta into the Gulf
of Guinea. On its way through Mali, it crosses a vast floodplain region called the inland delta. The inland delta has an
average surface area of 73 000 km2 , and it dissipates a significant proportion of the flow of the river through absorption and evaporation (it is estimated that about 40 % of water
is lost through the inland delta by evaporation and/or infiltration; Andersen et al., 2005). From the headwaters to the
Niger Delta (taking into account the hydrologically active
area), the basin has an average area of about 1.5 million km2 .
The Niger River is shared by nine countries and is the main
source of water for about 100 million people living principally from agriculture and farming. During the 1970s and
1980s, West Africa faced extreme climate variations with
extended drought conditions followed by floods; therefore,
there is a need to better understand the functioning of this
basin for water management purposes. The complexity of
modeling the Niger Basin is mainly due to the fact that it
crosses very different climatic zones, from the tropical humid Guinean coast where it generally rains every month of
the year, to the desertic Saharan region. The main source of
water over the basin is due to the WAM which is characterized by a marked annual cycle and significant interannual
variability, leading to the succession of extreme events such
as droughts and floods. In addition to modeling issues due
to rainfall uncertainties, the representation of processes such
as infiltration and evaporation from floodplains is also very
important in modeling the Niger River.
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of subgrid hydrology in order to account for the heterogeneity of precipitation, topography and vegetation in each grid
cell. A TOPMODEL approach (Beven and Kirkby, 1979)
has been used to simulate a saturated fraction, fsat , over
which precipitation is entirely converted into surface runoff
(Decharme et al., 2006). Infiltration is computed via two
subgrid exponential distributions of rainfall intensity and
soil maximum infiltration capacity (Decharme and Douville,
2006). The TRIP original RRM was developed by Oki and
Sud (1998) at University of Tokyo. It was first used at MétéoFrance to convert the model simulated runoff into river discharge using a global river channel network at a 1◦ resolution. More recently, a 0.5◦ resolution global river network has been developed which is used for this study. The
TRIP schematic concept is presented in Fig. 2 and more
details can be found in Pedinotti et al. (2012). The ISBATRIP CHS was recently improved to take into account a
simple groundwater reservoir, which can be seen as a simple soil-water storage, and a variable stream flow velocity
computed via the Manning equation (Decharme et al., 2010).
In addition, ISBA-TRIP includes a two-way flood scheme in
which a flooded fraction of the grid cell can be determined
(Decharme et al., 2008, 2011). The flood dynamics are described through the daily coupling between the ISBA land
surface model and TRIP RRM, including a prognostic flood
reservoir. This reservoir fills when the river height exceeds
the critical river bank full height (Fig. 3a), hc (m). The flood
interacts with the soil hydrology through infiltration, with the
overlying atmosphere through precipitation interception and
through free-water-surface evaporation. For the Niger application, Pedinotti et al. (2012) added a simple, linear, confined
aquifer reservoir to account for the long-term water storage
in deep and more or less confined aquifers. This reservoir
was built on the example of the groundwater reservoir, but
with a significantly longer time-delay factor. The confined
aquifer is supplied by a fraction (1 − α) of the drainage from
ISBA, the remaining fraction (α) going to the groundwater
reservoir.
2.3
Figure 3. The spatial distribution of river depth (m) (a), Manning
coefficient (b), and river width (m) (c) parameters in ISBA-TRIP.
2.2 Review of the ISBA-TRIP model
ISBA is a state-of-the-art land surface model which calculates the time evolution of the surface energy and water
budgets (Noilhan and Planton, 1989). It represents the natural land surface component of the SURface-EXternalized
(SURFEX) coupling platform at Météo-France (Masson et
al., 2013). In the current study, we use the three-layer forcerestore soil hydrology option (Boone et al., 1999). The options are also activated for a comprehensive representation
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TRIP specific parameters
The Manning coefficient characterizes the roughness so that
it modulates the surface water velocity and thus water levels
and discharge, via the Manning formula. However, it is difficult to estimate via in situ measurements or remote sensing
techniques. In ISBA-TRIP, the Manning friction coefficient,
nriv , varies linearly and proportionally to the river width, W
(m), from 0.04 near the river mouth to 0.1 (Decharme et al.,
2011) in the upstream grid cells (Fig. 3b):
Wmouth − W
,
(1)
nriv = nmin + (nmax − nmin )
Wmouth − Wmin
where nriv represents the grid cell average Manning coefficient, nmax and nmin the maximum and minimum values of
the Manning friction coefficient (equal to 0.1 and 0.04, reHydrol. Earth Syst. Sci., 18, 4485–4507, 2014
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V. Pedinotti et al.: Assimilation of SWOT data
spectively), Wmin (m) the minimum river width value and
Wmouth (m) is the width of the mouth in each basin of the
TRIP network (Wmouth = 2000 for the Niger Basin). W is an
important parameter because it controls both the river flow
speed and the floodplain dynamics. It is computed over the
entire TRIP network via an empirical mathematical formulation that describes a simple geomorphological relationship
between W and the mean annual discharge at each river cross
section (Knighton, 1998; Arora and Boer, 1999; Decharme et
al., 2011):
1/2
W = max 30, β × Qyr ,
(2)
where Qyr (m3 s−1 ) is the annual mean discharge in each grid
cell estimated using the global runoff database from Cogley (1979). As discussed in Decharme et al. (2011), the β coefficient can vary drastically from one basin to another. β is
equal to 20 for the branch of the river going from the river
mouth (5◦ N) to 12◦ N and is fixed to 10 for the remaining
river branch. The spatial distribution of the river width is
shown in Fig. 3c. Another critical parameter is the riverbankfull critical height, hc , which is computed according to the
river width via a simple power function (Decharme et al.,
2011):
hc = W 1/3 .
(3)
The spatial distribution of hc is shown in Fig. 3a. These relationships are found to work well at the global scale but can
lead to significant errors for a specific basin at the regional
scale (see the sensitivity tests in Pedinotti et al., 2012). Indeed, the assumption that the river width is proportional to
the annual mean discharge can lead to significant errors in
flooded areas where the river bed enlarges but the discharge
is reduced through the flooding process. Moreover, it is assumed that the Manning coefficient is only dependent on the
river width while other factors should be considered, such
as the presence of vegetation, debris, soil type, etc. Finally,
these parameters are defined as constant in time, which is a
significant assumption, especially in a region with a marked
seasonal climate variability such as the Niger Basin. Remote
sensing opens the possibility of estimating the river width by
direct measurements and the critical bank-full height by indirect algorithms (Pavelski and Smith, 2008; Yamazaki et al.,
2014; Durand et al., 2008). However, the Manning coefficient
will still be difficult to estimate even using remote sensing.
This study focuses on finding a methodology to estimate this
critical parameter via DA.
3
Satellite observations
The aim of this work is to estimate the potential benefits of
using SWOT satellite measurements to provide spatially distributed estimates of the Manning coefficient over the Niger
Hydrol. Earth Syst. Sci., 18, 4485–4507, 2014
River basin. This section describes this future satellite mission and how virtual SWOT observations have been generated in this study.
3.1
The SWOT mission
SWOT will provide high-resolution images of water surface
elevations over the oceans and continental surface water bodies. It will therefore observe continental surface waters at an
unprecedented resolution, providing information for a better
understanding of surface water dynamics and storage variations. The mission is currently planned to be launched around
2020.
The satellite main payload will be the Ka-band Radar Interferometer (KaRIN), a wide swath SAR (synthetic aperture
radar) interferometer. KaRIN will have two antennas separated by a 10 m boom, which will observe two ground swaths
of 60 km on each side of the satellite nadir, separated by a
20 km gap. The intrinsic pixel resolution will vary from 60
(near range) to 10 m (far range) across track and will be at
best around 5 m along track (however, this value is also dependent upon decorrelation time). Yet, for these intrinsic pixels, water elevation measurements have metric errors, which
increase along the swath (depending on the look angle). To
increase vertical accuracy, pixels have to be aggregated: over
a 1 km2 area inside the river mask, water elevation has a
10 cm or lower error (Rodríguez, 2012). River slopes will be
measured with a 1 cm km−1 resolution, after processing elevations over 10 km river reaches (Rodríguez, 2012). SWOT
will be able to observe rivers wider than 100 m (mission requirement) and should be able to observe rivers wider than
50 m (goal). The chosen orbit will be a low earth orbit with
a 78◦ inclination, in order to observe almost all of the continental surfaces (Rodríguez, 2012).
3.2
Observing system simulation experiment (OSSE)
and virtual SWOT data
The OSSE framework consists in simulating data that would
be observed by the future measurement platform using a numerical model, in order to use it as virtual observations for
DA experiments. The main objective of an OSSE is to validate the DA method by using ideal conditions. It is assumed
that the state of the system and the error statistics of the
model and observations are known and correctly described,
which is not the case in real conditions. This method is useful
within the framework of the SWOT satellite mission preparation, since it allows a quantification of the satellite data
contribution to improve large-scale river modeling (such as
for the Niger Basin) before the launch of the satellite. First,
a realistic modeling of the studied basin is needed for the
OSSE. The model must be able to simulate the major hydrodynamic processes of the basin so that the simulated observations will reasonably represent the reality. The ISBA-TRIP
setup evaluated in Pedinotti et al. (2012), with the inclusion
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Figure 4. Distribution of the “true” Manning coefficient over the
river. This distribution of Manning coefficients was used as an input
parameter to run the reference ISBA-TRIP model.
of the flooding scheme and aquifer reservoir, is used to represent the true state of the hydrological system, also referred
to as the reference simulation. For this so-called “truth”, the
model and its parameters are assumed to be perfect. An error
is then added to this true state to build virtual observations.
The background simulation results from the integration of
the same model in a different configuration, for instance with
a different set of parameters (also called perturbed or background parameters). It gives an a priori description of the
system that is an approximation of the truth. In the present
study focussed on parameter estimation, the purpose of the
DA algorithm is to retrieve an optimal set of model parameters starting with the background parameters, by assimilating the virtual observations. It is important to note that in
the present study, the error between the “true” Manning coefficients and the background Manning coefficients does not
vary in time.
Within the framework of this SWOT-dedicated study, the
true simulation is used to generate the SWOT observations,
with the help of a relatively simple simulator developed by
Biancamaria et al. (2011). Based on the prescribed orbit and
swath, the simulator provides an ensemble of SWOT tracks
and related dates. The SWOT tracks are provided for the orbital period and then repeated over the years 2002 and 2003
(assuming the satellite started its first orbit on 1 January
2002). The virtual data are the sum of the ISBA-TRIP water levels at the corresponding grid points and an instrumental error which is added to partially account for the SWOT
observation errors (see Sect. 4.2.1 for details). A river mask
for the Niger comprising grid cells with a river width above
200 m is defined as illustrated in Fig. 4, which displays the
Manning coefficient for the unmasked 110 pixels. It should
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be noted that the SWOT satellite will not measure water
depth but free-surface-water elevation. For DA applications
in real conditions, the direct comparison between SWOT and
ISBA-TRIP water levels will not be straightforward and will
need further investigation. Indeed, the SWOT satellite measures free-surface-water elevation, which cannot be directly
compared to the ISBA-TRIP outputs which are stream-water
absolute depths in the river channel. The assimilation then requires finding a way to compare these two different variables
in order to perform the DA. For example, they can be compared in terms of anomalies relative to a mean value over a
long period of time instead of absolute water elevations. This
method allows removing the bias due to different reference
values of the level where the water elevation is zero. However, in the framework of an OSSE, the same model is used
to generate the a priori and observed water levels and this
issue can be evaded.
The 22-day repeat orbit and the 140 km swath used in this
simulator allowed for a global coverage of the study domain
within 22 days. Among the available orbits, two orbits have
been preselected by the NASA–CNES project team, for various scientific and technical reasons (mainly to seek a compromise between both the hydrological and oceanographic
scientific communities). These two orbits have the same repeat period, but different altitudes, meaning different subcycles. The repeat period corresponds to the minimum time
taken by the satellite to fly over exactly the same ground location. Given the orbit parameters and earth’s rotational speed,
it requires a fixed number of satellite revolutions. For all of
these revolutions, the part of the orbit that goes from north
to south corresponds to the descending track and the one that
goes from south to north corresponds to the ascending track.
These ascending and descending tracks cross the Equator at
different times during one repeat period. The difference between these crossing times for two adjacent ascending (or
descending) tracks during a repeat period is the orbit subcycle. The 970 km altitude orbit has a 3-day subcycle, whereas
the 873 km altitude orbit has a 1-day subcycle. These two orbits both have global coverage but with a different time and
spatial spread of the satellite tracks during one repeat period.
The 1-day subcycle orbit has two adjacent swaths every day,
meaning that each river basin will be well sampled in few
days, but then there will be no observations for several days
(Fig. 5) with the risk of missing short-term events. The 3day subcycle orbit has two adjacent swaths every 3 days, on
average, meaning ground tracks will be more regularly distributed in space and time. Yet, there will be no tracks close in
time at any point during the cycle (Fig. 6). Thus, due to their
spatial and temporal coverage over the domain, these two orbits present specific advantages and disadvantages that will
be investigated within of the DA framework. The OSSE is
run over 2 years starting from the beginning of the monsoon
season, on 1 June 2002. During each SWOT 22-day repeat,
there are about 53 satellite overpasses on the Niger Basin for
the 3-day subcycle orbit and 50 for the 1-day subcycle orbit.
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Figure 5. The 22-day repeat, 871 km altitude, 1-day subcycle orbit coverage, data issued from the SWOT data simulator.
4 Data assimilation schemes
4.1 Choice of the control variable
The goal of using assimilation in this study is to correct the
TRIP routing input parameters which are associated with
uncertainties. The contribution of such corrections is estimated by comparing model outputs (water level, discharge,
water storage, etc.) with and without DA. Sensitivity tests in
Pedinotti et al. (2012) determined the most sensitive TRIP
parameters which impact the major hydrological processes
of the Niger Basin. It was shown that a modification of nriv
has a significant impact on the simulated hydrological variables over the Niger Basin which can be expected since the
Manning coefficient is used for flow calculations in the river
Hydrol. Earth Syst. Sci., 18, 4485–4507, 2014
stream, via the Manning formula. Due to its close relationship with water levels and discharge, it is one of the most
important empirical parameters in the field of hydrology and
hydraulics. Thus, a good estimation of this coefficient in
the river bed leads to a better reproduction of surface water dynamics. There is a tendency to regard the selection of
the Manning coefficient as an arbitrary or intuitive process.
Hydrodynamic modelers usually determine the value of the
Manning coefficient manually, often using estimations based
on visual interpretation of the land cover. The roughness can
also be described by geomorphologic relationships, which
are related to another parameter for which more information
is known (river width for example). In ISBA-TRIP, nriv is
assumed to vary linearly with W , from 0.04 near the river
mouth to 0.10 in the upstream grid cells (Eq. 1). These geowww.hydrol-earth-syst-sci.net/18/4485/2014/
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Figure 6. As in Fig. 5, except for a 22-day repeat, 970 km altitude, 3-day subcycle orbit average.
morphologic relationships are used to obtain the spatially distributed Manning coefficient which provides a “global” fit or
best estimate. However, the accuracy of these relations can be
very uncertain due to the significant heterogeneity of the river
and land properties, especially in uncalibrated models. Both
approaches can lead to significant errors over a large computational domain which is characterized by multiple land
use/cover classes. Although progress in remote sensing will
probably improve our estimates of the Manning coefficient
(using the two aforementioned approaches), this parameter
will not be estimated directly via remote sensing and therefore will remain dependent on the physical relevance of the
geomorphologic relationships. Thus, DA appears to be an appealing option for estimating the Manning coefficient using
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remote sensing data. In reality, the temporal variability of
the error on the Manning coefficient is related to the flow
dynamics as the river bed morphology can be significantly
modified by flood events. Even though this temporal variability is not accounted for in our OSSE framework, the DA
analysis is performed sequentially over a 2-day time window
which allows for a high variability of the correction on the
Manning coefficient. It should be noted that in a real case
study where sources of uncertainty are multiple (contrary to
our OSSE framework where errors are only due to Manning
coefficient perturbations), correcting the Manning coefficient
could be interpreted as a way to account for other uncertainties (which are possibly characterized by errors with a higher
temporal variability than that of the Manning coefficient).
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Figure 7. Schematic of the assimilation scheme used in this study. The black line represents the a priori or background trajectory and the
blue line is the posterior trajectory after data assimilation. After the DA step, the a priori trajectory is represented by a dashed line to compare
with the new trajectory.
The choice of the time window length could be revisited in
further studies. However, a longer assimilation window also
requires a bigger disc storage capacity and this must be considered when selecting the length of the assimilation window.
In the following section, along-track virtual SWOT data
over 2 days are assimilated to correct the Manning coefficient for the unmasked nt = 110 ISBA-TRIP grid points. For
each analysis at time t (also called cycle), the control vector is thus a vector of 110 elements noted x t . The framework of the OSSE does not guarantee the physical representativeness of the modeled values, specifically because of the
lack of monitoring data. Here, the values have therefore simply been bounded to be within a reasonable range (based on
rivers similar to the Niger and the scale of TRIP).
4.2
The extended Kalman filter (EKF)
The assimilation algorithm used for the calculation of the
analysis is the EKF, which is presented in this section within
the framework of parameter optimization. The true Manning
coefficients (known in the framework on an OSSE but unknown in reality) are gathered in the vector x true
of size nt .
t
The vector of the a priori parameters x bt for the hydrological models is prescribed by geomorphologic relationships
which induce an error tb = x true
− x bt of which statistics are
t
described in the background error covariance matrix B. Here,
these statistics are assumed to be constant over the assimilation cycles and to follow a Gaussian distribution, centered on
0 with a standard deviation, σtb , of 20 % of the average value
of the Manning coefficient over the river.
The observation vector y 0t of dimension pt contains all
the SWOT observations collected during the 2-day assimilation window. The observation operator H projects the control
vector onto the observation space. This operator is nonlinear
as it is the composition of the hydrological model M and
of a selection operator S that simply extracts or interpolates
the simulated water levels (over the whole gridded domain)
at the observation points. Here H = SoM, where S represents the SWOT simulator and M is the integration of the
hydrological model over the assimilation window. The relation yt = H (x t ) allows describing the true water level vector ytrue
at the observation points when x true
is used and the
t
t
background hydrological water level vector ybt at the observation points when x bt is used. In OSSE, an observation error
t0 is added to y true
to account for instrumental and repret
sentativeness errors. The observation errors are assumed to
be decorrelated in space and time, and the observation error
standard deviation (σt0 )2 is set equal to (σtb )2 . The observation error covariance matrix Rt is thus assumed to be diagonal. Further work should focus on a complete estimation of
the observation error statistics in order to allow for alongtrack correlation of the instrumental errors (Lion, 2012).
The EKF analysis vector x at is defined as a correction to
the background vector, where the the innovation vector d t =
y 0t − Ht (x bt ) is multiplied by the gain matrix Kt :
x at = x bt + Kt d t ,
(4)
where Kt reads
Kt = Bt HTt (Ht Bt Ht T + Rt )−1 ,
(5)
where Ht is the tangent linear of H with respect to x t .
The statistics of the analysis error ta are determined by the
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Table 1. Principal variables, vectors and matrices used in the data
assimilation of SWOT water levels (WL). The assimilation window
length is N days. The number p of observed water levels during the
assimilation window changes for each cycle.
Symbol
Variable
Dimensions
y 0t
Observation vector, containing
the SWOT WL observations during
the N day assimilation window
p (different for each
assimilation cycle)
x bt
Background vector, containing the
corrupted Manning coefficient
over the river mask
n = 110
x at
Analysis vector, containing the
corrected values of the Manning
coefficient over the river mask
n = 110
Mt
ISBA-TRIP (nonlinear)
Ht (x bt )
ISBA-TRIP simulated water levels,
using x bt as an input parameter
p
Rt
Observation error covariance matrix
(related to water levels)
p×p
Bt
Background error covariance matrix
(related to the Manning coefficient)
n×n
At
Analysis error covariance matrix
n×n
Ht
Jacobian matrix of H (sensitivity of
ISBA-TRIP water levels
to the Manning coefficient)
n×p
Kt
Ht,ij =
∂H
H(x t + 1x) − H(x t − 1x)i
=
∂x |t,ij
1xt,j
=
Gain matrix
analysis covariance matrix At =(I−Kt Ht )Bt (Bouttier and
Courtier, 1999). The analysis vectors provide the corrected
Manning coefficient values, which can then can be used to
integrate the hydrological model and simulate the analyzed
water levels over the whole domain. A schematic diagram of
the assimilation process is shown in Fig. 7, and the key variables are represented in Eqs. (4) and (5) and listed in Table 1.
4.3
Figure 8. The Manning coefficient relative error averaged over the
river versus time with a 1-day subcycle (green) and a 3-day subcycle (blue) orbit SWOT assimilation. The related error is calculated
as the ratio |nrivwith/without assi − nrivtruth | / nrivtruth , where nriv is the
Manning coefficient.
Jacobian matrix calculation
The EKF algorithm relies on the computation of a local approximation of the tangent linear of the observation operator that describes the relationship between the control vector
and the observation space, with respect to the control vector. As the size of the control space is limited in this study, a
finite difference scheme can be used to perform this approximation, in the vicinity of the background vector. Since the
observation operator H includes the model propagation, the
calculation of the Jacobian matrix Ht requires the computation of nt independent integrations of the hydrological model
with a perturbed element for each component of x t .
(6)
−
1y +
t,i − 1y t,i
−
1x +
t,j + 1x t,j
In Eq. (6), H translates the variations of water levels at
the observation points induced by the variation of Manning
−
coefficients. 1y +
t,i and 1y t,i represent the water level variations at the gridded pixel “i” related to variations 1x +
t,j and
1x −
of
the
Manning
coefficient
at
the
gridded
pixel
“j”.
t,j
A centered finite difference scheme was favored over a onesided scheme as it reduces noise on the evaluation of the local
derivative. The computation of Ht thus requires 2 × nt integrations of ISBA-TRIP over the assimilation window using
elementary perturbed Manning coefficients at the unmasked
observation point. The computational cost of H could be
optimized as only perturbations on Manning coefficients at
the grid points located upstream of each observation point
have an impact on water level at the observation point. In
the present work, the 2 × nt integrations of ISBA-TRIP are
achieved sequentially.
5
Results
The impact of DA on the hydrological processes is analyzed
using the relative error. For any variable v, the relative error
is expressed as
v − vtruth ,
errv = (7)
v
truth
where vtruth refers to the variable v as described in the true
simulation.
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Figure 9. The Manning coefficient distribution (a) for the truth, (b) the background, (c) the 1-day subcycle assimilation at the end of the
assimilation period (after 289 assimilation cycles in December 2003) and (d) the 3-day subcycle assimilation at the end of the assimilation
period (after 289 assimilation cycles in December 2003).
5.1
Impact of assimilation on Manning coefficient
The truth simulation is made using Manning coefficients
which are constant in time, meaning that there is no temporal variation of the error on the model parameters; thus, it
is expected that the DA analysis leads to a constant value of
the corrected Manning close to the “true” values.
However, since the Manning coefficient is spatially distributed, several spatial combinations of these parameters
might resolve the assimilation problem which is generally
referred to as the equifinality hypothesis. Figure 8 shows the
Manning coefficient relative error (averaged over the river)
time series for the two orbits. The average relative error
of the Manning coefficient is significantly improved during
the assimilation period and tends to converge to a stable
value (about 0.19 for the 1-day subcycle orbit and 0.17 for
the 3-day subcycle orbit), since the error is not significantly
changed from January 2003 until the end of the assimilation
experiment. The convergence towards the minimum value of
the spatially averaged relative error to the true averaged Manning coefficient is slightly faster for the 3-day subcycle orbit
than for the 1-day subcycle.
Figure 9 displays the spatial distribution of the Manning
coefficient (a) for the truth, (b) the background simulation,
(c) the 1-day subcycle assimilation at the end of the study period and (d) the 3-day assimilation at the end of the study period. The general patterns of the Manning coefficient distribution are recovered through the DA; especially, the extreme
Hydrol. Earth Syst. Sci., 18, 4485–4507, 2014
values of the background distribution are corrected. Also, we
notice that the values downstream are better corrected than
those upstream of the river, which can be expected since the
downstream grid cells take advantage of the cumulated corrections upstream.
The Manning coefficient temporal evolution at the eight
gage locations is shown in Fig. 10. It should be noted that
in some places and for both subcycles, the “real” Manning
coefficient value is only approached and not found through
the assimilation cycles, which can be related to the equifinality problem. The 1-day subcycle and 3-day subcycle orbit
assimilations converge to the same value in five locations out
of eight. In Banankoro, Kandadji and Malanville, however,
the coefficient values for the two orbits converge to different
values. Banankoro is located upstream of the river, so this
difference can be explained by the lack of data upstream of
this location for obtaining a robust estimate of the Manning
coefficient at this site. Also, the impact of the Manning coefficient on the simulation depends on the rain amount over the
observed locations. According to the considered subcycle,
the satellite will see different zones and a different number
of observations corresponding to different rain events which
can lead to the different values obtained for the optimal Manning coefficient in some locations. Also, a “jump” with a frequency of about 20 days is observed in every location and for
the two subcycles and might be related to the orbit repetitivity.
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Figure 10. Manning coefficient versus assimilation cycle at eight locations (Fig. 1) for the 3-day subcycle (blue) and 1-day subcycle (green)
orbits. The value of the true coefficient is in red.
Table 2. Water level relative error averaged over the river and at the location of the eight gages along the river (each gage is defined by its
number specified inside the orange rectangles in Fig. 1). The relative error is calculated as the ratio (hwith/without assi − htruth ) / htruth , where
h is the water level (m); assi: assimilation, 3 and 1 d sbc: 3- and 1-day subcycles.
Location
no.
River
mean
1
2
3
4
5
6
7
8
No assi
3 d sbc
1 d sbc
0.45
0.12
0.12
0.35
0.09
0.19
0.17
0.25
0.10
0.36
0.11
0.11
0.55
0.17
0.12
0.16
0.12
0.13
0.69
0.12
0.07
0.68
0.10
0.12
1.10
0.09
0.18
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Figure 11. Water level relative error averaged over the river versus
time with no assimilation (black), with 1-day subcycle (green) and
3-day subcycle (blue) orbit SWOT assimilations. The relative error
is calculated as the ratio |hwith/without assi − htruth | / htruth , where h
is the water level (m).
5.2
Impact of assimilation on water levels
Table 2 gives the water level mean relative error computed
with respect to the true water levels, first averaged over the
entire river for the 2-year period and then at each of the eight
observing stations shown in Fig. 1. Figures 11 and 12 display the water level relative error averaged over the river and
at the eight observing stations as a function of time when (i)
there is no assimilation (black curve), (ii) after a 1-day subcycle orbit SWOT-observation assimilation (green curve) and
(iii) the 3-day subcycle orbit SWOT-observation assimilation
(blue curve).
These results show that the DA analysis leads to a significant reduction of the water level relative error over the whole
river (the averaged relative error is reduced by more than a
factor of 3 with DA) and at the eight gages. In most of the
eight locations, there is an improvement of several meters
reaching up to 9 m at Lokoja (for an 8 m averaged river depth
along the river). As for the Manning coefficient, a noise with
a repeat period of 20 days is observed and can be directly related to the noise observed on the Manning coefficient. Also,
even in the locations where the analyzed Manning coefficient
differs for both subcycles, the same water levels are retrieved
for both subcycles, which confirms the equifinality hypothesis.
A great improvement in the water level is achieved with
the first assimilation cycles since the background Manning
parameters and thus the background water levels initially differ significantly from the true parameter values and water
levels. For the following cycles, as the background parameters are set equal to the analysis parameters, the sequential correction results in a convergence towards the optimal
Manning coefficients leading to water levels that are coherent with the true water levels. The improvement is larger for
stations that are located downstream of the river, possibly
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because of the cumulated corrections upstream of these stations. Moreover, the hypothesis of a linear relation between
width and roughness means that the 20 % standard deviation
will lead to a larger absolute error on the roughness for wider
rivers. These results are similar for both orbits as illustrated
in Fig. 13, which shows the spatially distributed relative error of water levels averaged over the period from June 2002
to December 2003 for the run with (a) no assimilation, (b)
a 3-day subcycle assimilation and (c) a 1-day subcycle assimilation. Without assimilation, the relative error over the
river ranges between 0 and 1.2. With assimilation, more than
90 % of the river pixels have a relative error smaller than 0.2
for both subcycles, and no pixel has a relative error higher
than 0.5.
5.3
Impact of assimilation on river discharge
Table 3 presents the discharge mean relative error computed
with respect to the true discharge, first averaged over the entire river for the 2-year period and then at each of the eight
observing stations shown in Fig. 1. Figures 14 and 15 display
the discharge relative error averaged over the river and the
discharge evolution at the eight observing stations as a function of time when (i) there is no assimilation (black curve),
(ii) after a 1-day subcycle orbit SWOT-observation assimilation (green curve) and (iii) the 3-day subcycle orbit SWOTobservation assimilation (blue curve). The assimilation contributes to an improvement of the river discharge over the
whole basin and at the eight locations, although this improvement is smaller than for water levels which can be expected
since the Manning roughness is updated through level measurements. Discharge improvement, even if less significant
than for water levels, can represent several hundreds of cubic
meters per second globally and up to 3000 m3 s−1 in Lokoja.
Discharge obtained after assimilation is somewhat “noisy”
(as observed for water level) for both orbits during the wet
season. This is likely due to a higher discharge sensitivity to
Manning coefficient change during this period. Discharge is
improved, in particular, at Lokoja, i.e., the location situated
furthest downstream of the river, which is a promising result
for coupled land–ocean applications since it shows that the
RRM can provide a reasonable estimation of discharge at the
river mouth. Similar to what was found for water levels, there
is almost no discharge sensitivity to the considered orbit.
Figure 16 shows the spatially distributed relative error of
discharge averaged over the period June 2002–December
2003 for the run without assimilation (a), 3-day subcycle assimilation (b) and 1-day subcycle assimilation (c). The discharge relative error is globally improved with better results
over the inner delta for the 1-day subcycle orbit. Otherwise,
there is no significant difference in results between the two
orbits. Without assimilation, the relative error range over the
river goes from 0 to 0.4. With assimilation, all pixels have
a relative error smaller than 0.2, with 80 % of them having
errors of less than 0.1.
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Figure 12. Time evolution of water levels at the eight locations shown in Fig. 1 for the “truth” (red curves), with no assimilation (black
curves) and with assimilation of SWOT 1-day subcycle (green) and 3-day subcycle (blue) orbit observations.
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Table 3. Discharge relative error averaged over the river and at the location of the eight gages along the river (each gage is defined by its
number specified inside the orange rectangles in Fig. 1). The relative error is calculated as the ratio (qwith/without assi − qtruth ) / qtruth , where
q is the discharge (m3 s−1 ).
Location
no.
River
mean
1
2
3
4
5
6
7
8
No assi
3 d sbc
1 d sbc
0.14
0.08
0.07
0.06
0.04
0.03
0.10
0.04
0.03
0.18
0.11
0.09
0.22
0.14
0.13
0.20
0.14
0.13
0.20
0.14
0.11
0.15
0.09
0.08
0.14
0.06
0.06
Figure 14. Discharge relative error averaged over the river versus
time with no assimilation (black), with 1-day subcycle (orange) and
3-day subcycle (blue) orbit SWOT assimilations. The relative error
is calculated as the ratio (|qwith/without assi −qtruth | / qtruth , where q
is the water level (m3 s−1 ).
Figure 13. Relative error of water levels averaged over the period
of assimilation.
Hydrol. Earth Syst. Sci., 18, 4485–4507, 2014
To better understand the relationship between the water
levels and the discharge, the flooded fraction time series at
two locations (Ke Macina and Lokoja) is shown in Fig. 17.
In Ke Macina, there was no flooded fraction before the assimilation, while there was about 15–20 % for the “truth”. At
this location, DA leads to a water level increase that generates flooding for both orbits, in agreement with the true run.
The amplitude of the flooded fraction simulated with the assimilation for a 3-day subcycle is close to that of the true run
while the flooded fraction simulated with assimilation for a
1-day cycle is overestimated. This results because the water
level and discharge results slightly overestimate the results
from the true run for the 1-day orbit.
Another interesting case is observed in Lokoja, where the
model simulates flooding in 25 % of the grid area with no assimilation, which is not observed for the “truth”. Here again,
by reducing water levels, the assimilation considerably reduces the flooded fraction for the 1-day subcycle orbit and
even prevents it from occurring for the 3-day subcycle orbit. No floods are modeled at the other sites for the truth,
the run with no assimilation or the runs with assimilation, so
these sites are not shown in Fig. 17. These results are valuable since they show that the use of DA corrects the flood
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Figure 15. Time evolution of discharge at the location of the eight locations (Fig. 1) for the “truth” (red curves), with no assimilation (black
curves) and with assimilation of SWOT 1-day subcycle (green) and 3-day subcycle (blue) orbit observations.
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Figure 17. Flooded fraction versus time at Ke Macina and Lokoja,
for the truth (red), with no assimilation (black), with assimilation
for 3-day subcycles (blue) and 1-day subcycles (green). Note that in
Lokoja, there is no flooded fraction represented for the truth and for
the run with assimilation with a 3-day subcycle.
Figure 16. Relative error of discharge averaged over the period of
assimilation.
prediction for two major sites of the Niger Basin. Indeed, Ke
Macina is located just upstream to the entrance of the innerdelta region, while Lokoja is the last in situ station upstream
of the river outlet. It should be noted that the discharge response to water level modification depends on whether or
not there are floods. For example, at Ke Macina, during the
monsoon period, the water level is increased via assimilation, which results in a better fit with the truth simulation and
in a discharge decrease. This is coherent with the results of
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plains leads to a reduction of the discharge. However, in regions without floodplains, a water level increase leads to a
discharge increase (see Kandadji for example).
The frequency of events as a function of the flooded fraction value (ratio of flooded area over pixel area) is shown
in Fig. 18 for the truth (a), without assimilation (b), a 1day subcycle assimilation (c) and a 3-day subcycle assimilation (d). Only the pixels with a flooded fraction greater
than 10 % (0.1 on the horizontal axis) are considered. It is
shown that without assimilation, the model does not simulate flooded fractions above 0.5, which represents about 8 %
of the flood events for the truth simulation. Moreover, without assimilation, the model tends to overestimate the occurrence of smaller events. This is corrected by the assimilation,
with a slight tendency to over-estimate flood intensity for the
assimilation with the 3-day subcycle orbit, while the 1-day
subcycle orbits leads to an excessive occurrence of flooded
fractions contained in the [0.2–0.3] range. According to these
results, DA allows for a better simulation of the water storage variations and leads to better estimation of flood event
occurrence and intensity in the inner-delta area.
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Figure 18. Frequency of flood events over the delta classified by intensity (flooded fraction). Only the pixels with a flooded fraction higher
than 10 % are considered for the calculation.
5.4
Water storage variations
Ideally, for water resource management applications and for
making reliable future water resource projections, global hydrologic models should be able to reasonably simulate water
storage variations in regional to large-scale continental reservoirs including rivers, groundwater, aquifers and floodplains.
It is then of interest to see if DA can improve the simulation of these water variations. Figure 19 shows the relative
water storage variations in four continental reservoirs (river,
floodplains, aquifers and soil) for the truth (red), without assimilation (black), 1-day subcycle (blue) and 3-day subcycle
assimilations (green). For each reservoir, the 20-day running
average water storage variations are divided by the averaged
water storage over the period of assimilation. The maximum
relative water storage variation ranges from 6 % in the river
reservoir to about 30 % in the floodplain reservoir, which is
not negligible. In the four reservoirs, the simulations with assimilation better represent the amplitude and the phase of the
water storage variations. The assimilation seems to be useful
for better representing anomalies in continental reservoirs,
which are subject to many uncertainties. However, it should
be noted that the physical representativeness of these storage
values is not guaranteed due to the lack of monitoring data.
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6 Discussion
Optimization of the Manning coefficient using a DA methodology leads to a significant improvement of the water levels over the Niger River, and also at the eight locations with
gages. The relative error of the Manning coefficient is reduced (40 % reduction) and it globally converges towards an
optimal value despite potential problems related to equifinality. The relative error of the water level is globally improved
(a 30 % reduction) and the amplitude of the water level is
closer to the truth with assimilation than without assimilation. Discharge is also improved by the assimilation, but to
a lesser extent than for the water levels (7 %). Moreover, the
proposed methodology results in a better prediction of flood
event occurrence and intensity in the inner delta and better
simulates water storage anomaly maxima and minima in several reservoirs, especially the groundwater and the aquifer
reservoirs, for which the temporal evolution is difficult to observe. This study is promising since, to our knowledge, no
large-scale assimilation applications exist for the optimization of spatially distributed hydrological parameters. It shows
SWOT observations would be useful for the improvement of
CHSs. This method could lead to a better representation of
the water cycle in climate prediction applications, but could
also be used for large-scale water resource management applications. Finally, there is no clear advantage difference between the two subcycle orbits used for this study; each has
better skill for certain situations.
Hydrol. Earth Syst. Sci., 18, 4485–4507, 2014
4504
V. Pedinotti et al.: Assimilation of SWOT data
Figure 19. Relative water storage variations in the river, the floodplains, the aquifer and the soil reservoirs for the truth (red), no assimilation
(black), 1-day orbit subcycle (green) and 3-day subcycle assimilations (blue). For each reservoir, the 20-day running average water variations
are divided by the averaged water storage over the period of assimilation (from June 2002 to December 2003).
This study has some limitations and several assumptions
should be noted. The assumption of the white noise error for
SWOT observations is probably too optimistic. Furthermore,
no correlation of the measurement errors along the swath has
been assumed. Estimating satellite observation error sources
has been the subject of several studies at the French space
agency (CNES) in recent years. Initially, a white noise was
introduced within the SWOT water level along track altimetric estimate in order to represent the error due to satellite observations (Biancamaria et al., 2011). Lion (2012) presents
methods to simulate, in a more realistic manner, different
sources of SWOT satellite observation errors. These errors
are generally due to several factors such as satellite attitude,
baseline error, phase unwrapping errors, etc. These errors
are not always Gaussian and do not always have a mean
value of 0. A perspective for improvement of the assimilation methodology proposed in this study is to introduce these
errors into the assimilation system in order to get a more realistic estimation of SWOT observation errors and of the error covariance matrix R. However, their introduction in the
system is not obvious and requires the use of a different assimilation filter due to the aforementioned Gaussian issue.
Indeed, the Gaussian error distribution along SWOT tracks
does not ensure that the error of the observation vector, y 0 , is
Hydrol. Earth Syst. Sci., 18, 4485–4507, 2014
Gaussian. Yet, the Gaussian nature of the observation error is
a strong assumption of the EKF and possible solutions to get
around this limitation exist, such as the use of an ensemble
Kalman filter or a particle filter.
The hypothesis that the Manning coefficient uncertainties
are the only source of model errors is obviously a rather simple assumption since other errors, such as those related to
precipitation forcing uncertainties, riverbank-full depth error
or the relatively simple ISBA-TRIP physics, can also be the
sources of significant modeling errors. It could be potentially
interesting to perform the assimilation on an ensemble of perturbed runs in order to take into account several uncertainty
scenarios and the estimation of the background modeling matrix could be done using an ensemble method (Evensen et al.,
2004). Within the framework of a real-data experiment, accounting for various sources of errors via Manning control
will lead to improved Manning values that should not be interpreted as physical values. Modeling assumptions also put
a limitation on the DA performance in the context of realdata experiments. For example, it is assumed in the TRIP
model that geomorphological parameters such as the Manning coefficient are constant in time, which is a significant
assumption, especially in a region with a strong seasonal climate variability, such as the Niger Basin. Hopefully, SWOT
www.hydrol-earth-syst-sci.net/18/4485/2014/
V. Pedinotti et al.: Assimilation of SWOT data
observations will help to correct this problem, for example,
using this method to build seasonal climatologies of key parameters. To exploit this possibility, a further OSSE study
could be done, in which the “true” Manning coefficient varies
seasonally.
Additionally, this study was done within the context of
OSSE, in which the truth was issued from a reference
ISBA-TRIP simulation. This allowed for an evaluation of
the methodology but makes the improvements on roughness, level, flow and storage highly correlated. Moreover,
the OSSE does not guarantee the physical representativeness
of the corrected values of the Manning coefficient since the
background and the observations are issued from the same
model. For these reasons, the performance of the DA will
need to be re-evaluated with real observations. In the study
presented here, the truth and the perturbation are based on
the same physical parameterizations: this is not true when
real data are used. Therefore, the assimilation should be applied using either real observations of water level, or water
level issued from a different model, such as a hydrodynamic
model. In further studies, longer assimilation windows could
be exploited but also require a bigger storage capacity which
must be considered for the choice of the assimilation window
size.
Finally, this method must be applied to other ISBA-TRIP
parameters and for other large-scale basins to evaluate its
global application capability. It is not guaranteed that a
methodology, which works for a specific basin, could be used
for all other major basins (with different climates, geology,
etc.). Ongoing work is focused on applying the methodology
herein to other basins. These proposed improvements aim at
ensuring that the assimilation methodology will be applicable when real SWOT data area be available.
7
Conclusions
This study presents a simple method for assimilating SWOT
virtual water level into a large-scale coupled land-surface hydrology model (TRIP-ISBA) in order to improve estimates of
the required global hydrological model input parameters. In
this case, the assimilation is used for the correction of a single parameter which is the Manning coefficient. To accomplish this, an OSSE was performed, using virtual SWOT observations of water levels. Two orbits, with different subcycles but with the same 22-day repeat period, have been considered to generate the observations (1-day and 3-day subcycles), each one providing a specific spatial and temporal
coverage of the domain. Uncertainties on the estimation of
the Manning coefficient are assumed to be the only sources
of modeling errors. The EKF algorithm was applied every 2
days (the length of the assimilation window) to compute an
optimal Manning coefficient (analysis). The Manning coefficient globally converged for both orbital subcycles to the
same average value, the convergence being faster for the 3www.hydrol-earth-syst-sci.net/18/4485/2014/
4505
day subcycle orbit. The method leads to a global reduction
of 40 % of the Manning coefficient error over the river. This
correction significantly improved the water levels (the error
has been reduced by 30 % for the river) and, to a lesser extent, discharge (7 % of reduction of the error which can be
significant for the Niger River in terms of water resources
considering that its mean annual discharge is 6000 m3 s−1 ).
Moreover, the biggest improvements were observed downstream of the river (Lokoja), which is a valuable result for climate applications which require estimation of the discharge
at large river mouths.
This method gives a promising perspective for globalscale applications, and it could be extended to other large
basins. However, several relatively simple hypotheses have
been made, and these should be addressed and refined in future studies. The context of the OSSE allows for the evaluation of the model but does not guarantee the physical representativeness of the corrected values obtained in this study.
Moreover, other sources of uncertainties should be assumed
for the assimilation, such as rainfall errors and/or riverbankfull depth. Modeling errors such as those from the ISBA land
surface parameterization should be considered, such as that
pertaining to runoff. It was also considered in this work that
observation and modeling errors were not correlated in space
and time, which might not be realistic. The use of more realistic errors simulated by Lion (2012) in the framework of the
SWOT mission prelaunch investigations will be considered
in future studies.
Another perspective consists in the application of this
method to other TRIP parameters, or several parameters at a
time. Correction of ISBA parameters, such as those controlling subgrid runoff for example, is also planned but must be
considered carefully as the impact on the river is less direct.
Before the satellite launch, the AirSWOT airborne campaign
will provide SWOT-like data sets of water level, which will
enable studies using a more realistic SWOT DA application,
instead of the observing simulation system experiment presented here. Even if this airborne campaign does not cover
the Niger Basin, it will potentially provide a better observation error model. Yet, using more complex observations and
model errors might require a modification of the assimilation
scheme to overcome extremely stringent EKF filter assumptions of Gaussian unbiased errors. Possible assimilation techniques to test are the ensemble Kalman filter or the particle
filter.
Acknowledgements. This work is supported by the African Monsoon Multidisciplinary Analysis (AMMA) project and the Surface
Water Ocean Topography (SWOT) satellite mission project of the
Centre National d’Etudes Spatiales (CNES). The diverse studies
presented in this paper would not have been possible without the
valuable contribution of the Autorite du Bassin du Niger(ABN).
Edited by: F. Tian
Hydrol. Earth Syst. Sci., 18, 4485–4507, 2014
4506
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